Matt Whitaker, a former federal prosecutor, is reportedly set to be sworn in as acting attorney general on Wednesday evening, just hours after the president announced Sessions had handed in his resignation.
"Most importantly as my time as attorney general, we have restored and upheld the rule of law", Mr Sessions added, while thanking the Republican president.
The Justice Department has the ultimate authority over Mueller's investigation into Russia's alleged interference in the 2016 presidential election and interactions between Trump associates and Russian officials. Since the day I was honored to be sworn in as Attorney General of the United States, I came to work at the Department every day determined to do my duty and serve my country.
He also said Mr Sessions' replacement might reduce Mr Mueller's budget "so low that his investigation grinds nearly to a halt".
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Whitaker continued, "If he were to continue to investigate the financial relationships without a broadened scope in his appointment, then this would raise serious concerns that the special counsel's investigation was a mere witch hunt".
With the midterms over, Special Counsel Robert Mueller is believed to be preparing fresh indictments against Trump campaign figures, possibly including his son Donald Trump Jr. and a former campaign consultant Roger Stone, and could press for the president himself to answer questions.
Last year Whitaker, who was a legal analyst for CNN as well as former US attorney, wrote that he felt the Mueller investigation had gone too far in looking into Trump Organization financial records that were not related to the 2016 election. But with Sessions's resignation, that's changing. He is a conservative who has written op-eds in the past suggesting that the Mueller Investigation of Trump and the 2016 election has gone "too far", and has also run for elected office three times in the past, all times as a Republican. He said it would spark a "constitutional crisis" if Trump forced out Sessions as a "prelude" to ending or limiting Mueller's investigation.
Rosenstein has opposed firing Mueller, to Trump's chagrin.